Visual complex analysis

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Bibliographic Information

Visual complex analysis

Tristan Needham

Clarendon Press , Oxford University Press, 1998

  • : pbk

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Note

Includes bibliographical references (p. [573]-578), and index

Description and Table of Contents

Description

Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians.

Table of Contents

  • 1. Geometry and Complex Arithmetic
  • 2. Complex functions as Transformations
  • 3. Mobius Transformations and Inversion
  • 4. Differentiation: The Amplitwist Concept
  • 5. Further Geometry of Differentiation
  • 6. Non-Euclidean Geometry
  • 7. Winding Numbers and Topology
  • 8. Complex Integration: Cuachy's Theorem
  • 9. Cauchy's Formula and Its Applications
  • 10. Vector Fields: Physics and Topology
  • 11. Vector Fields and Complex Integration
  • 12. Flows and Harmonic Functions

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